Best Known (82, 106, s)-Nets in Base 8
(82, 106, 2731)-Net over F8 — Constructive and digital
Digital (82, 106, 2731)-net over F8, using
- net defined by OOA [i] based on linear OOA(8106, 2731, F8, 24, 24) (dual of [(2731, 24), 65438, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(8106, 32772, F8, 24) (dual of [32772, 32666, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(8106, 32773, F8, 24) (dual of [32773, 32667, 25]-code), using
- 1 times truncation [i] based on linear OA(8107, 32774, F8, 25) (dual of [32774, 32667, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(8101, 32768, F8, 23) (dual of [32768, 32667, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(81, 6, F8, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- 1 times truncation [i] based on linear OA(8107, 32774, F8, 25) (dual of [32774, 32667, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8106, 32773, F8, 24) (dual of [32773, 32667, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(8106, 32772, F8, 24) (dual of [32772, 32666, 25]-code), using
(82, 106, 26408)-Net over F8 — Digital
Digital (82, 106, 26408)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8106, 26408, F8, 24) (dual of [26408, 26302, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(8106, 32773, F8, 24) (dual of [32773, 32667, 25]-code), using
- 1 times truncation [i] based on linear OA(8107, 32774, F8, 25) (dual of [32774, 32667, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(8101, 32768, F8, 23) (dual of [32768, 32667, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(81, 6, F8, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- 1 times truncation [i] based on linear OA(8107, 32774, F8, 25) (dual of [32774, 32667, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8106, 32773, F8, 24) (dual of [32773, 32667, 25]-code), using
(82, 106, large)-Net in Base 8 — Upper bound on s
There is no (82, 106, large)-net in base 8, because
- 22 times m-reduction [i] would yield (82, 84, large)-net in base 8, but